Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, q\neq 0$. $\dfrac{{(p^{-4})^{3}}}{{(p^{2}q^{5})^{-2}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{-4}}$ to the exponent ${3}$ . Now ${-4 \times 3 = -12}$ , so ${(p^{-4})^{3} = p^{-12}}$ In the denominator, we can use the distributive property of exponents. ${(p^{2}q^{5})^{-2} = (p^{2})^{-2}(q^{5})^{-2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{-4})^{3}}}{{(p^{2}q^{5})^{-2}}} = \dfrac{{p^{-12}}}{{p^{-4}q^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-12}}}{{p^{-4}q^{-10}}} = \dfrac{{p^{-12}}}{{p^{-4}}} \cdot \dfrac{{1}}{{q^{-10}}} = p^{{-12} - {(-4)}} \cdot q^{- {(-10)}} = p^{-8}q^{10}$.